Algebra Tutorials!
Rational Expressions
Graphs of Rational Functions
Solve Two-Step Equations
Multiply, Dividing; Exponents; Square Roots; and Solving Equations
Solving a Quadratic Equation
Systems of Linear Equations Introduction
Equations and Inequalities
Solving 2nd Degree Equations
Review Solving Quadratic Equations
System of Equations
Solving Equations & Inequalities
Linear Equations Functions Zeros, and Applications
Rational Expressions and Functions
Linear equations in two variables
Lesson Plan for Comparing and Ordering Rational Numbers
Solving Equations
Radicals and Rational Exponents
Solving Linear Equations
Systems of Linear Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
Solving Quadratic Equations
Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
Systems of Linear Equations
Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
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The Quadratic Equation

8.4 The Discriminate

Need To Know
▪ Review the Quadratic Formula
▪ The Discriminate
▪ Predicting roots
▪ Writing equations from solutions

The Quadratic Formula

For ax2 + bx + c = 0,

The Discriminate is ________________

The Discriminate

Discriminate Nature of Solutions
Positive –
Perfect Squar
Positive –
Not a perfect

Predicting the Solution Type

Determine what type of solution each has.

x2 – 7x + 5 = 0

x2 + 4x + 6 = 0

9t2 – 48t + 64 = 0


8.6 Graphing the Quadratic Eq.

Need To Know
▪ Graph quadratic equation
▪ Finding the vertex and axis of symmetry
▪ Vertex Form of an equation

Graph f (x) = ax2: The effect of “a”?

Label vertex point, use axis of sym.

a > 1, then parabola is _________
a < 1, then parabola is _________
a < 0, then parabola is _________

The Graph of f (x) = a(x – h)2


Label vertex point, use axis of sym.

(x+h) h is neg, then parabola _________
(x–h) h is pos, then parabola _________
The effect of h is _________

The Graph of f (x) = a(x – h)2 + k


Label vertex point, use axis of sym.

The vertex is _________
The equation of the A.O.S. _________
The effect of k _________

Graphing y = a(x – h)2 + k


Summarize the Vertex Form

y = a(x – h)2 + k is the Vertex Form.

Three parameters: a, h, k

Maximum or Minimum


8.7 More about Graphing Quadratics

Need To Know
▪ Review completing the square
▪ Converting into Vertex Form
(not to learn but to appreciate the short cut formula)
▪ Vertex Point Formula – Short Cut
▪ Finding intercepts
▪ Sketching the graph of a quadratic

Completing the Square


x2 – 10x + _______ =


y = a(x – h)2 + k
What is the vertex point? ____________

Convert Quadratics to Vertex Form

If the quadratic is in standard form, we have no information.
We need to change the form into vertex form (squared stuff).

g(x) = x2 – 10x + 21
f(x) = 4x2 + 8x - 3

Vertex Point – short cut (easy way)

If f(x) = ax2 + bx + c, then (h, k) = ___________
which means _____________________________.
1. Find h with the formula
2. Find k by plugging h into the function.

g(x) = x2 – 10x + 21
f(x) = 4x2 + 8x – 3

Intercept Points

X-intercept point = point where graph crosses x-axis. (a, 0)
Find the x-intercept point by letting y = 0.

Y-intercept point = point where graph crosses y-axis. (0, b)
Find the y-intercept point by letting x = 0.

Find the intercepts of f(x) = x2 + 5x – 6

Sketch Graph

y = x2 + 6x + 5
Label vertex point,
Label intercept points

Sketch Graph

y = -3x2 + 6x + 2

Label vertex point,
Label intercept points


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